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Advances in Mathematical Physics

Volume 2011 (2011), Article ID 870613, 9 pages

http://dx.doi.org/10.1155/2011/870613

Research Article

## The Central Extension Defining the Super Matrix Generalization of

Famaf-CIEM, Universidad Nacional de Córdoba, Ciudad Universitaria, 5000 Cordoba, Argentina

Received 13 June 2011; Accepted 1 August 2011

Academic Editor: Andrei D. Mironov

Copyright © 2011 Carina Boyallian and Jose I. Liberati. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- H. Awata, M. Fukuma, Y. Matsuo, and S. Odake, “Representation theory of ${W}_{1+\infty}$ algebra,” in
*Proceedings of the Workshop Quantum Field Theory, Integrable Models and Beyond*, T. Inami, et al., Ed., Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan, February 1994. - H. Awata, M. Fukuma, Y. Matsuo, and S. Odake, “Representation theory of ${W}_{1+\infty}$ algebra,”
*Progress of Theoretical Physics Supplement*, vol. 118, pp. 343–373, 1995. View at Google Scholar - I. Bakas, B. Khesin, and E. Kiritsis, “The logarithm of the derivative operator and higher spin algebras of ${W}_{\infty}$ type,”
*Communications in Mathematical Physics*, vol. 151, no. 2, pp. 233–243, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - V. Kac and A. Radul, “Quasifinite highest weight modules over the Lie algebra of differential operators on the circle,”
*Communications in Mathematical Physics*, vol. 157, no. 3, pp. 429–457, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - C. N. Pope, L. J. Romans, and X. Shen, “Ideals of Kac-Moody algebras and realisations of ${W}_{\infty}$,”
*Physics Letters B*, vol. 245, no. 1, pp. 72–78, 1990. View at Publisher · View at Google Scholar - H. Awata, M. Fukuma, Y. Matsuo, and S. Odake, “Quasifinite highest weight modules over the super ${W}_{1+\infty}$ algebra,”
*Communications in Mathematical Physics*, vol. 170, no. 1, pp. 151–179, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - E. Bergshoeff, M. Vasiliev, and B. de Wit, “The super-${W}_{\infty}(\lambda )$ algebra,”
*Physics Letters B*, vol. 256, no. 2, pp. 199–205, 1991. View at Publisher · View at Google Scholar - S. Odake and T. Sano, “${W}_{1+\infty}$ and super-${W}_{\infty}$ algebras with SU(N) symmetry,”
*Physics Letters B*, vol. 258, no. 3-4, pp. 369–374, 1991. View at Publisher · View at Google Scholar - S. Odake, “Unitary representations of
*W*infinity algebras,”*International Journal of Modern Physics A*, vol. 7, no. 25, pp. 6339–6355, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - L. Guieu and C. Roger,
*L'Algèbre et le Groupe de Virasoro*, Aspects Géométriques et Algébriques, Généralisations, Les Publications CRM, Montreal, Canda, 2007. - A. O. Radul, “Lie algebras of differential operators, their central extensions and
*W*-algebras,”*Functional Analysis and Its Applications*, vol. 25, no. 1, pp. 25–39, 1991. View at Publisher · View at Google Scholar - C. Boyallian, V. G. Kac, J. I. Liberati, and C. H. Yan, “Quasifinite highest weight modules over the Lie algebra of matrix differential operators on the circle,”
*Journal of Mathematical Physics*, vol. 39, no. 5, pp. 2910–2928, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - S.-J. Cheng and W. Wang, “Lie subalgebras of differential operators on the super circle,”
*Research Institute for Mathematical Sciences Publications*, vol. 39, no. 3, pp. 545–600, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - V. G. Kac and J. I. Liberati, “Unitary quasi-finite representations of ${W}_{\infty}$,”
*Letters in Mathematical Physics*, vol. 53, no. 1, pp. 11–27, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - C. Boyallian, V. G. Kac, and J. I. Liberati, “On the classification of subalgebras Cend
_{N}and gc_{N},”*Journal of Algebra*, vol. 260, no. 1, pp. 32–63, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - V. Kac,
*Vertex Algebras for Beginners*, vol. 10 of*University Lecture Series*, American Mathematical Society, Providence, RI, USA, 2nd edition, 1998. - V. G. Kac, “Formal distribution algebras and conformal algebras,” in
*XIIth International Congress of Mathematical Physics (ICMP '97) (Brisbane)*, pp. 80–97, Internat Press, Cambridge, Mass, USA, 1999. View at Google Scholar - W. L. Li, “2-cocyles on the algebra of differential operators,”
*Journal of Algebra*, vol. 122, no. 1, pp. 64–80, 1989. View at Publisher · View at Google Scholar - W. Li and R. L. Wilson, “Central extensions of some Lie algebras,”
*Proceedings of the American Mathematical Society*, vol. 126, no. 9, pp. 2569–2577, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - D. Liu and N. Hu, “Derivation algebras and 2-cocycles of the algebras of
*q*-differential operators,”*Communications in Algebra*, vol. 32, no. 11, pp. 4387–4413, 2004. View at Publisher · View at Google Scholar